(3x+5)(5x-2)=0

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Solution for (3x+5)(5x-2)=0 equation: 


Simplifying
(3x + 5)(5x + -2) = 0

Reorder the terms:
(5 + 3x)(5x + -2) = 0

Reorder the terms:
(5 + 3x)(-2 + 5x) = 0

Multiply (5 + 3x) * (-2 + 5x)
(5(-2 + 5x) + 3x * (-2 + 5x)) = 0
((-2 * 5 + 5x * 5) + 3x * (-2 + 5x)) = 0
((-10 + 25x) + 3x * (-2 + 5x)) = 0
(-10 + 25x + (-2 * 3x + 5x * 3x)) = 0
(-10 + 25x + (-6x + 15x2)) = 0

Combine like terms: 25x + -6x = 19x
(-10 + 19x + 15x2) = 0

Solving
-10 + 19x + 15x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -3x)(2 + -5x) = 0


Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

Subproblem 2
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {-1.666666667, 0.4}

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